Banach-Stone-like results for combinatorial Banach spaces

摘要

We show that under a certain topological assumption on two compact hereditary families F and g on some infinite cardinal kappa, the corresponding combinatorial spaces XF and XG are isometric if and only if there is a permutation of kappa inducing a homeomorphism between F and g. We also prove that two different regular families F and g on omega cannot be permuted one to the other. Both these results strengthen the main result of [5].